 Solution

ID: past-exam-of-the-theoretical-physics-i-course-of-the-university-of-cambridge/2018/1/d/solution

With no electric field, the power relation from part (a) gives

\frac{d}{d t} (γm c^{2}) = e v \cdot (v \times B) = 0.

Consequently

γ (t) = γ_{0}, ∣ v (t) ∣ = ∣ v_{0} ∣.

The magnetic part of the relativistic Lorentz force changes the direction of mechanical momentum, but performs no work. This conclusion does not require the magnetic field to be spatially uniform: it follows from the local orthogonality of

v

and

v \times B

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